nonlinear patterns

Hello, I have an exercise and I am a bit confused. We have to consider a bifurcation in a pentagonal box with symmetry group D5 (What does this really means?) and then work out what patterns can arise if the bifurcation is governed by:
i)the 1-dimensional non trivial representation
ii)the natural representation of D5.

And then we need to sketch the patterns in each case, and especially for the one dimensional we need to work out the type of bifurcation giving arise to the pattern.

There is also a hint : to write the elements of D5 in terms of a reflection and a rotation.